91Ó°ÊÓ

Gibbs free energy, often denoted as \( G \), is an essential concept in thermodynamics, particularly when discussing spontaneous processes. It combines the concepts of enthalpy, entropy, and temperature. The formula for Gibbs free energy is given by \( G = H - TS \), where \( H \) is enthalpy, \( T \) is temperature, and \( S \) is entropy.
Gibbs free energy is a measure of the maximum reversible work that a system can perform at constant temperature and pressure. When we talk about changes in \( G \), we usually refer to whether a process can occur spontaneously. The change in Gibbs free energy, \( \mathrm{dG} \), helps us predict the direction of a process.

• If \( \mathrm{dG} < 0 \), the process is spontaneous.
• If \( \mathrm{dG} = 0 \), the system is in equilibrium.
• If \( \mathrm{dG} > 0 \), the process is non-spontaneous.

In the context of the exercise, for an irreversible process at constant \( T \) and \( P \), \( \mathrm{dG} \) must be negative for the process to be spontaneous, supporting option b.

Entropy, usually symbolized as \( S \), is a measure of disorder or randomness in a system. It reflects the number of ways the system can be arranged at a microscopic level.
According to the second law of thermodynamics, the total entropy of an isolated system can never decrease; it either increases or remains constant. This principle helps us understand irreversible processes. In an irreversible process, the entropy change of the universe \( (dS_{universe}) \) is always greater than zero.
Within the exercise, we recognize that the irreversible process occurring causes a net increase in entropy, meaning \( \mathrm{dS} > 0 \). This aligns perfectly with the second law and reinforces why option b is the correct choice for the problem. An increase in entropy reflects the natural tendency towards disorder, a key aspect of irreversible processes.

Thermodynamics is the study of energy, heat, and work in physical systems. The laws of thermodynamics provide a statistical account of how and why energy transfer occurs, and what limitations exist for the processes.
There are four laws of thermodynamics which govern the energetics of all physical systems:

• **Zeroth Law**: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
• **First Law**: Energy cannot be created or destroyed, only transferred or converted. This is often summarized as the principle of the conservation of energy.
• **Second Law**: The total entropy of an isolated system can never decrease over time. It highlights the directional flow of energy transformations.
• **Third Law**: As the temperature of a system approaches absolute zero, the entropy of the system approaches a constant minimum.

In reference to the exercise, understanding the second law is crucial, as it dictates that entropy increases in irreversible processes, providing the solution needed for choosing the correct option.